KEY CONCEPTS A mortgage is an annuity where the present value is the amount borrowed to purchase a home The amortization period is the length of time needed to eliminate the debt Typical amortization period for mortgages are 20 to 25 years; typical amortization periods for personal loans are 1 to 5 years *** For all Canadian mortgages, interest is compounded semi-annually and payments are usually made monthly To access the Int and Prn commands on the TVM solver, press APPS 1:Finance then cursor down to the command and press ENTER
EXAMPLE 1 Paying a Mortgage Kara recently bought her first home for $255 000. As a firsttime homebuyer, Kara can make a 5% down payment on the house and take out a mortgage for the remaining balance. Her mortgage broker found a bank offering an annual interest rate of 5.49%, compounded semi-annually for a 5 year fixed rate mortgage on an amortization period of 25 years. 5 / 100 = 0.05 (a) Calculate the downpayment Downpayment = Value of the house x % down payment = 255 000 x 0.05 = $12 750 (b) Calculate the amount to be mortgaged (ie. the remaining amount) Remaining balance = Value of the house downpayment = 255 000 12 750 = $242 250
EXAMPLE 1 Paying a Mortgage Kara recently bought her first home for $255 000. As a firsttime homebuyer, Kara can make a 5% down payment on the house and take out a mortgage for the remaining balance. Her mortgage broker found a bank offering an annual interest rate of 5.49%, compounded semi-annually for a 5 year fixed rate mortgage on an amortization period of 25 years. (b) Calculate the amount to be mortgaged (ie. the remaining amount) Remaining balance = $242 250 (c) Use the TVM solver to determine the monthly payment [do not clear the data you will need it for Parts (e) and (f)] Mortgage is entered as Monthly payment present is value based on the amortization Mortgage period is a loan Must be paid immediately! N = I% = PV = PMT = FV = P/Y = C/Y = 12 300x 25 5.49 242250 0 0 1477.26 12 2 Press ALPHA then ENTER Kara s monthly mortgage payment is $1477.26
EXAMPLE 1 Paying a Mortgage (d) Calculate the total amount paid over 5 years 12 monthly payments x 5 years = 60 payments Recall PMT = $1477.26 (from previous question) Total amount paid = n x PMT = # of payments x payment amount = 60 x 1477.26 = 88 635.60 A total of $88 635.60 was paid over 5 years (e) Calculate the total interest paid over 5 years (use the A: Int function) 60 62 410.35 Int(1,,2) = # of monthly payments in 5 years Total interest paid over 5 years is $62 410.35 Negative value represents that money is being paid out (f) Calculate the total principal paid over 5 years (use the 0: Prn function) 60 26 225.25 Prn(1,,2) = # of monthly payments in 5 years The total amount paid towards the value of the house is $26 225.25
EXAMPLE 1 Paying a Mortgage (g) Calculate the approximate value of Kara s house after 5 years if it has an appreciation rate of 5% per year 5 / 100 = 0.05 Appreciation rate Rate at which the value of an item increases over time New value = Original value x (1 + rate of appreciation) Number of years = 255 000 x (1 + 0.05) 5 = 255 000 x (1.05) 5 = 255 000 x 1.2763 = 325 451.80 The new value of the house is $325 451.80
EXAMPLE 2 Reading an Amortization Table for a Mortgage Consider the amortization table for the first year of a $368 000 mortgage (a) Calculate the monthly payment Add Principal Paid and Interest Paid (b) Calculate the total amount paid in the first year (c) What do you notice about the values in the Principal Paid column? The values are increasing $27 705
EXAMPLE 2 Reading an Amortization Table for a Mortgage Consider the amortization table for the first year of a $368 000 mortgage (d) Calculate the total principal paid after the first year (e) What do you notice about the values in the Interest Paid column? The values are decreasing (f)calculate the total interest paid after the first year $6827.53 $20877.47 $27705 Amount going towards the value of the house
EXAMPLE 2 Reading an Amortization Table for a Mortgage Consider the amortization table for the first year of a $368 000 mortgage (g) How much debt is owed on the house (ie. balance remaining) at the end of 1 year? Balance = Value of the house Total principal paid towards house = 368 000 6827.53 = 361 172.47 The remaining balance to be paid towards the value of the house is $361 172.47 $6827.53 $20877.47 $27705 Amount going towards the value of the house
HOMEWORK (Using graphing calculator) Page 425 #1, 3 5, 7